Pandas Profiling Report

Dataset statistics

Number of variables	10
Number of observations	5695
Missing cells	0
Missing cells (%)	0.0%
Duplicate rows	0
Duplicate rows (%)	0.0%
Total size in memory	467.2 KiB
Average record size in memory	84.0 B

Variable types

Numeric	10

Alerts

`gross_revenue` is highly correlated with `invoiceno` and 3 other fields	High correlation
`recencydays` is highly correlated with `invoiceno`	High correlation
`invoiceno` is highly correlated with `gross_revenue` and 4 other fields	High correlation
`quantity` is highly correlated with `gross_revenue` and 3 other fields	High correlation
`frequency` is highly correlated with `invoiceno`	High correlation
`qtd_return` is highly correlated with `invoiceno`	High correlation
`avg_basket_size` is highly correlated with `gross_revenue` and 2 other fields	High correlation
`avg_unique_basket_size` is highly correlated with `gross_revenue` and 2 other fields	High correlation
`gross_revenue` is highly correlated with `invoiceno` and 1 other fields	High correlation
`invoiceno` is highly correlated with `gross_revenue` and 1 other fields	High correlation
`quantity` is highly correlated with `gross_revenue` and 1 other fields	High correlation
`avg_ticket` is highly correlated with `qtd_return`	High correlation
`qtd_return` is highly correlated with `avg_ticket`	High correlation
`avg_basket_size` is highly correlated with `avg_unique_basket_size`	High correlation
`avg_unique_basket_size` is highly correlated with `avg_basket_size`	High correlation
`gross_revenue` is highly correlated with `invoiceno` and 2 other fields	High correlation
`invoiceno` is highly correlated with `gross_revenue` and 1 other fields	High correlation
`quantity` is highly correlated with `gross_revenue` and 1 other fields	High correlation
`frequency` is highly correlated with `invoiceno`	High correlation
`avg_basket_size` is highly correlated with `gross_revenue` and 1 other fields	High correlation
`customerid` is highly correlated with `recencydays`	High correlation
`gross_revenue` is highly correlated with `invoiceno` and 3 other fields	High correlation
`recencydays` is highly correlated with `customerid`	High correlation
`invoiceno` is highly correlated with `gross_revenue` and 1 other fields	High correlation
`quantity` is highly correlated with `gross_revenue` and 1 other fields	High correlation
`avg_ticket` is highly correlated with `gross_revenue` and 1 other fields	High correlation
`qtd_return` is highly correlated with `gross_revenue` and 1 other fields	High correlation
`avg_basket_size` is highly correlated with `avg_unique_basket_size`	High correlation
`avg_unique_basket_size` is highly correlated with `avg_basket_size`	High correlation
`gross_revenue` is highly skewed (γ1 = 21.33147068)	Skewed
`avg_ticket` is highly skewed (γ1 = 53.30430577)	Skewed
`qtd_return` is highly skewed (γ1 = 51.46514451)	Skewed
`customerid` has unique values	Unique
`qtd_return` has 4143 (72.7%) zeros	Zeros

Reproduction

Analysis started	2022-09-20 10:01:24.384375
Analysis finished	2022-09-20 10:03:02.019253
Duration	1 minute and 37.63 seconds
Software version	pandas-profiling v3.1.0
Download configuration	config.json

customerid
Real number (ℝ_≥0)

HIGH CORRELATION
UNIQUE

Distinct	5695
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	31232.13942

Minimum	12346
Maximum	83709
Zeros	0
Zeros (%)	0.0%
Negative	0
Negative (%)	0.0%
Memory size	66.7 KiB

Quantile statistics

Minimum	12346
5-th percentile	12699.1
Q1	14288.5
median	16229
Q3	18210.5
95-th percentile	82731.1
Maximum	83709
Range	71363
Interquartile range (IQR)	3922

Descriptive statistics

Standard deviation	28408.38395
Coefficient of variation (CV)	0.909588151
Kurtosis	-0.5185359982
Mean	31232.13942
Median Absolute Deviation (MAD)	1962
Skewness	1.210180524
Sum	177867034
Variance	807036278.5
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
17850	1	< 0.1%
16344	1	< 0.1%
12922	1	< 0.1%
82097	1	< 0.1%
16589	1	< 0.1%
13730	1	< 0.1%
16866	1	< 0.1%
82095	1	< 0.1%
82094	1	< 0.1%
82093	1	< 0.1%
Other values (5685)	5685	99.8%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
12346	1	< 0.1%
12347	1	< 0.1%
12348	1	< 0.1%
12349	1	< 0.1%
12350	1	< 0.1%
12352	1	< 0.1%
12353	1	< 0.1%
12354	1	< 0.1%
12355	1	< 0.1%
12356	1	< 0.1%

Value	Count	Frequency (%)
83709	1	< 0.1%
83708	1	< 0.1%
83707	1	< 0.1%
83706	1	< 0.1%
83705	1	< 0.1%
83704	1	< 0.1%
83700	1	< 0.1%
83699	1	< 0.1%
83696	1	< 0.1%
83695	1	< 0.1%

gross_revenue
Real number (ℝ_≥0)

HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION
SKEWED

Distinct	5461
Distinct (%)	95.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	1862.766266

Minimum	0.42
Maximum	280206.02
Zeros	0
Zeros (%)	0.0%
Negative	0
Negative (%)	0.0%
Memory size	89.0 KiB

Quantile statistics

Minimum	0.42
5-th percentile	13.635
Q1	244.605
median	639.89
Q3	1653.865
95-th percentile	5522.757
Maximum	280206.02
Range	280205.6
Interquartile range (IQR)	1409.26

Descriptive statistics

Standard deviation	7963.897229
Coefficient of variation (CV)	4.275306771
Kurtosis	594.1773042
Mean	1862.766266
Median Absolute Deviation (MAD)	501.75
Skewness	21.33147068
Sum	10608453.88
Variance	63423659.07
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
7.95	9	0.2%
1.25	8	0.1%
4.95	8	0.1%
2.95	8	0.1%
12.75	7	0.1%
3.75	7	0.1%
1.65	7	0.1%
7.5	6	0.1%
5.95	6	0.1%
4.25	6	0.1%
Other values (5451)	5623	98.7%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.42	1	< 0.1%
0.65	1	< 0.1%
0.79	1	< 0.1%
0.84	3	0.1%
0.85	3	0.1%
1.07	1	< 0.1%
1.25	8	0.1%
1.44	1	< 0.1%
1.65	7	0.1%
1.69	1	< 0.1%

Value	Count	Frequency (%)
280206.02	1	< 0.1%
259657.3	1	< 0.1%
194550.79	1	< 0.1%
168472.5	1	< 0.1%
143825.06	1	< 0.1%
124914.53	1	< 0.1%
117379.63	1	< 0.1%
91062.38	1	< 0.1%
81024.84	1	< 0.1%
77183.6	1	< 0.1%

recencydays
Real number (ℝ_≥0)

HIGH CORRELATION
HIGH CORRELATION

Distinct	304
Distinct (%)	5.3%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	116.7311677

Minimum	0
Maximum	373
Zeros	38
Zeros (%)	0.7%
Negative	0
Negative (%)	0.0%
Memory size	89.0 KiB

Quantile statistics

Minimum	0
5-th percentile	3
Q1	22.5
median	71
Q3	199
95-th percentile	337.3
Maximum	373
Range	373
Interquartile range (IQR)	176.5

Descriptive statistics

Standard deviation	111.5236412
Coefficient of variation (CV)	0.955388723
Kurtosis	-0.6387979375
Mean	116.7311677
Median Absolute Deviation (MAD)	61
Skewness	0.8160444818
Sum	664784
Variance	12437.52255
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
1	110	1.9%
4	105	1.8%
3	98	1.7%
2	92	1.6%
10	86	1.5%
8	82	1.4%
9	80	1.4%
17	79	1.4%
7	78	1.4%
22	65	1.1%
Other values (294)	4820	84.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	38	0.7%
1	110	1.9%
2	92	1.6%
3	98	1.7%
4	105	1.8%
5	52	0.9%
7	78	1.4%
8	82	1.4%
9	80	1.4%
10	86	1.5%

Value	Count	Frequency (%)
373	23	0.4%
372	22	0.4%
371	17	0.3%
369	4	0.1%
368	13	0.2%
367	16	0.3%
366	15	0.3%
365	19	0.3%
364	11	0.2%
362	7	0.1%

invoiceno
Real number (ℝ_≥0)

HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION

Distinct	59
Distinct (%)	1.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	3.49165935

Minimum	1
Maximum	210
Zeros	0
Zeros (%)	0.0%
Negative	0
Negative (%)	0.0%
Memory size	89.0 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	1
median	1
Q3	4
95-th percentile	11.3
Maximum	210
Range	209
Interquartile range (IQR)	3

Descriptive statistics

Standard deviation	6.868852155
Coefficient of variation (CV)	1.96721715
Kurtosis	308.5962454
Mean	3.49165935
Median Absolute Deviation (MAD)	0
Skewness	13.32902721
Sum	19885
Variance	47.18112993
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
1	2855	50.1%
2	831	14.6%
3	508	8.9%
4	386	6.8%
5	243	4.3%
6	172	3.0%
7	143	2.5%
8	98	1.7%
9	68	1.2%
10	54	0.9%
Other values (49)	337	5.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	2855	50.1%
2	831	14.6%
3	508	8.9%
4	386	6.8%
5	243	4.3%
6	172	3.0%
7	143	2.5%
8	98	1.7%
9	68	1.2%
10	54	0.9%

Value	Count	Frequency (%)
210	1	< 0.1%
201	1	< 0.1%
124	1	< 0.1%
97	1	< 0.1%
93	1	< 0.1%
91	1	< 0.1%
86	1	< 0.1%
74	1	< 0.1%
63	1	< 0.1%
62	1	< 0.1%

quantity
Real number (ℝ_≥0)

HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION

Distinct	57
Distinct (%)	1.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	9.479543459

Minimum	1
Maximum	102
Zeros	0
Zeros (%)	0.0%
Negative	0
Negative (%)	0.0%
Memory size	89.0 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	5
median	9
Q3	13
95-th percentile	20
Maximum	102
Range	101
Interquartile range (IQR)	8

Descriptive statistics

Standard deviation	6.638745978
Coefficient of variation (CV)	0.7003233865
Kurtosis	18.41590315
Mean	9.479543459
Median Absolute Deviation (MAD)	4
Skewness	2.545936511
Sum	53986
Variance	44.07294816
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
7	443	7.8%
9	424	7.4%
1	420	7.4%
10	403	7.1%
6	391	6.9%
8	386	6.8%
5	360	6.3%
11	344	6.0%
4	294	5.2%
12	284	5.0%
Other values (47)	1946	34.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	420	7.4%
2	250	4.4%
3	248	4.4%
4	294	5.2%
5	360	6.3%
6	391	6.9%
7	443	7.8%
8	386	6.8%
9	424	7.4%
10	403	7.1%

Value	Count	Frequency (%)
102	1	< 0.1%
82	1	< 0.1%
79	1	< 0.1%
74	1	< 0.1%
69	1	< 0.1%
60	1	< 0.1%
59	1	< 0.1%
58	1	< 0.1%
56	1	< 0.1%
54	1	< 0.1%

avg_ticket
Real number (ℝ_≥0)

HIGH CORRELATION
HIGH CORRELATION
SKEWED

Distinct	5507
Distinct (%)	96.7%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	54.61760545

Minimum	0.42
Maximum	77183.6
Zeros	0
Zeros (%)	0.0%
Negative	0
Negative (%)	0.0%
Memory size	89.0 KiB

Quantile statistics

Minimum	0.42
5-th percentile	3.465
Q1	8.510502308
median	16.12
Q3	22.57508013
95-th percentile	76.32
Maximum	77183.6
Range	77183.18
Interquartile range (IQR)	14.06457782

Descriptive statistics

Standard deviation	1281.098642
Coefficient of variation (CV)	23.45578191
Kurtosis	2955.510013
Mean	54.61760545
Median Absolute Deviation (MAD)	7.217
Skewness	53.30430577
Sum	311047.263
Variance	1641213.73
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
3.75	11	0.2%
4.95	10	0.2%
1.25	9	0.2%
2.95	9	0.2%
7.95	8	0.1%
8.25	7	0.1%
12.75	7	0.1%
1.65	7	0.1%
4.15	6	0.1%
3.35	6	0.1%
Other values (5497)	5615	98.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.42	2	< 0.1%
0.535	1	< 0.1%
0.65	1	< 0.1%
0.79	1	< 0.1%
0.8371428571	1	< 0.1%
0.84	2	< 0.1%
0.85	3	0.1%
1.002222222	1	< 0.1%
1.02	1	< 0.1%
1.03875	1	< 0.1%

Value	Count	Frequency (%)
77183.6	1	< 0.1%
56157.5	1	< 0.1%
13305.5	1	< 0.1%
4453.43	1	< 0.1%
3861	1	< 0.1%
3096	1	< 0.1%
2027.86	1	< 0.1%
1687.2	1	< 0.1%
1377.077778	1	< 0.1%
1001.2	1	< 0.1%

frequency
Real number (ℝ_≥0)

HIGH CORRELATION
HIGH CORRELATION

Distinct	1225
Distinct (%)	21.5%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	0.5475706259

Minimum	0.005449591281
Maximum	17
Zeros	0
Zeros (%)	0.0%
Negative	0
Negative (%)	0.0%
Memory size	89.0 KiB

Quantile statistics

Minimum	0.005449591281
5-th percentile	0.01102941176
Q1	0.02492211838
median	1
Q3	1
95-th percentile	1
Maximum	17
Range	16.99455041
Interquartile range (IQR)	0.9750778816

Descriptive statistics

Standard deviation	0.5505967909
Coefficient of variation (CV)	1.005526529
Kurtosis	138.7856997
Mean	0.5475706259
Median Absolute Deviation (MAD)	0
Skewness	4.851371477
Sum	3118.414715
Variance	0.3031568261
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
1	2879	50.6%
2	48	0.8%
0.0625	18	0.3%
0.02777777778	17	0.3%
0.02380952381	16	0.3%
0.09090909091	15	0.3%
0.08333333333	15	0.3%
0.02941176471	14	0.2%
0.03448275862	14	0.2%
0.07692307692	13	0.2%
Other values (1215)	2646	46.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.005449591281	1	< 0.1%
0.005464480874	1	< 0.1%
0.005479452055	1	< 0.1%
0.005494505495	1	< 0.1%
0.005586592179	2	< 0.1%
0.005602240896	1	< 0.1%
0.005617977528	2	< 0.1%
0.00566572238	1	< 0.1%
0.005681818182	2	< 0.1%
0.005698005698	3	0.1%

Value	Count	Frequency (%)
17	1	< 0.1%
4	1	< 0.1%
3	5	0.1%
2	48	0.8%
1.142857143	1	< 0.1%
1	2879	50.6%
0.75	1	< 0.1%
0.6666666667	3	0.1%
0.550802139	1	< 0.1%
0.5335120643	1	< 0.1%

qtd_return
Real number (ℝ_≥0)

HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION
SKEWED
ZEROS

Distinct	219
Distinct (%)	3.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	48.01720808

Minimum	0
Maximum	80995
Zeros	4143
Zeros (%)	72.7%
Negative	0
Negative (%)	0.0%
Memory size	89.0 KiB

Quantile statistics

Minimum	0
5-th percentile	0
Q1	0
median	0
Q3	1
95-th percentile	40
Maximum	80995
Range	80995
Interquartile range (IQR)	1

Descriptive statistics

Standard deviation	1475.325676
Coefficient of variation (CV)	30.72493664
Kurtosis	2713.85495
Mean	48.01720808
Median Absolute Deviation (MAD)	0
Skewness	51.46514451
Sum	273458
Variance	2176585.85
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	4143	72.7%
1	190	3.3%
2	156	2.7%
3	107	1.9%
4	90	1.6%
6	72	1.3%
5	64	1.1%
12	49	0.9%
8	49	0.9%
7	48	0.8%
Other values (209)	727	12.8%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	4143	72.7%
1	190	3.3%
2	156	2.7%
3	107	1.9%
4	90	1.6%
5	64	1.1%
6	72	1.3%
7	48	0.8%
8	49	0.9%
9	38	0.7%

Value	Count	Frequency (%)
80995	1	< 0.1%
74215	1	< 0.1%
9361	1	< 0.1%
9014	1	< 0.1%
8060	1	< 0.1%
4627	1	< 0.1%
3768	1	< 0.1%
3335	1	< 0.1%
2975	1	< 0.1%
2160	1	< 0.1%

avg_basket_size
Real number (ℝ_≥0)

HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION

Distinct	2375
Distinct (%)	41.7%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	0.04377848893

Minimum	1.347436502 × 10^-5
Maximum	1
Zeros	0
Zeros (%)	0.0%
Negative	0
Negative (%)	0.0%
Memory size	89.0 KiB

Quantile statistics

Minimum	1.347436502 × 10^-5
5-th percentile	0.001363210568
Q1	0.003448275862
median	0.006622516556
Q3	0.0133742249
95-th percentile	0.25
Maximum	1
Range	0.9999865256
Interquartile range (IQR)	0.009925949037

Descriptive statistics

Standard deviation	0.1516964889
Coefficient of variation (CV)	3.465091934
Kurtosis	28.77128418
Mean	0.04377848893
Median Absolute Deviation (MAD)	0.003846281132
Skewness	5.278378743
Sum	249.3184945
Variance	0.02301182474
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
1	110	1.9%
0.5	71	1.2%
0.3333333333	53	0.9%
0.25	50	0.9%
0.2	36	0.6%
0.1666666667	28	0.5%
0.08333333333	26	0.5%
0.01	21	0.4%
0.01369863014	21	0.4%
0.009433962264	20	0.4%
Other values (2365)	5259	92.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1.347436502 × 10^-5	1	< 0.1%
2.469227255 × 10^-5	1	< 0.1%
7.067637289 × 10^-5	1	< 0.1%
7.165376899 × 10^-5	1	< 0.1%
0.0001278118609	1	< 0.1%
0.0001664078101	1	< 0.1%
0.0001676727029	1	< 0.1%
0.0001923816853	1	< 0.1%
0.0002325581395	1	< 0.1%
0.0002336448598	1	< 0.1%

Value	Count	Frequency (%)
1	110	1.9%
0.6666666667	1	< 0.1%
0.5	71	1.2%
0.3333333333	53	0.9%
0.3	1	< 0.1%
0.25	50	0.9%
0.2	36	0.6%
0.1875	1	< 0.1%
0.1764705882	1	< 0.1%
0.1666666667	28	0.5%

avg_unique_basket_size
Real number (ℝ_≥0)

HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION

Distinct	1282
Distinct (%)	22.5%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	0.1326961552

Minimum	0.0008976660682
Maximum	1
Zeros	0
Zeros (%)	0.0%
Negative	0
Negative (%)	0.0%
Memory size	89.0 KiB

Quantile statistics

Minimum	0.0008976660682
5-th percentile	0.005704545455
Q1	0.02777777778
median	0.05555555556
Q3	0.1111111111
95-th percentile	0.6383116883
Maximum	1
Range	0.9991023339
Interquartile range (IQR)	0.08333333333

Descriptive statistics

Standard deviation	0.2213233687
Coefficient of variation (CV)	1.667895866
Kurtosis	8.64729026
Mean	0.1326961552
Median Absolute Deviation (MAD)	0.03514739229
Skewness	3.021774538
Sum	755.7046039
Variance	0.04898403353
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
1	271	4.8%
0.5	162	2.8%
0.3333333333	115	2.0%
0.07692307692	103	1.8%
0.1	97	1.7%
0.1111111111	96	1.7%
0.25	96	1.7%
0.2	95	1.7%
0.07142857143	95	1.7%
0.09090909091	94	1.7%
Other values (1272)	4471	78.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.0008976660682	1	< 0.1%
0.001335113485	1	< 0.1%
0.001367989056	1	< 0.1%
0.001386962552	1	< 0.1%
0.001418439716	1	< 0.1%
0.001455604076	1	< 0.1%
0.001479289941	1	< 0.1%
0.001481481481	1	< 0.1%
0.001510574018	1	< 0.1%
0.001533742331	1	< 0.1%

Value	Count	Frequency (%)
1	271	4.8%
0.8333333333	1	< 0.1%
0.8	1	< 0.1%
0.75	2	< 0.1%
0.6666666667	9	0.2%
0.6428571429	1	< 0.1%
0.6363636364	1	< 0.1%
0.6	4	0.1%
0.5454545455	1	< 0.1%
0.5263157895	1	< 0.1%

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

Count
Matrix

A simple visualization of nullity by column.

Nullity matrix is a data-dense display which lets you quickly visually pick out patterns in data completion.

First rows

	customerid	gross_revenue	recencydays	invoiceno	quantity	avg_ticket	frequency	qtd_return	avg_basket_size	avg_unique_basket_size
0	17850	5391.21	372	34	6	18.152222	17.000000	40.0	0.019619	0.114478
1	13047	3237.54	31	10	12	18.822907	0.028302	36.0	0.007189	0.058140
2	12583	7281.38	2	15	25	29.479271	0.040323	51.0	0.002964	0.060729
3	13748	948.25	95	5	8	33.866071	0.017921	0.0	0.011390	0.178571
4	15100	876.00	333	3	2	292.000000	0.073171	22.0	0.037500	1.000000
5	15291	4668.30	25	15	17	45.323301	0.040115	29.0	0.007133	0.145631
6	14688	5630.87	7	21	24	17.219786	0.057221	399.0	0.005800	0.064220
7	17809	5411.91	16	12	23	88.719836	0.033520	42.0	0.005834	0.196721
8	15311	60767.90	0	91	43	25.543464	0.243316	474.0	0.002383	0.038251
9	16098	2005.63	87	7	15	29.934776	0.024390	0.0	0.011419	0.104478

Last rows

	customerid	gross_revenue	recencydays	invoiceno	quantity	avg_ticket	frequency	avg_basket_size	avg_unique_basket_size
5685	83700	4839.42	1	1	25	78.055161	1.0	0.000931	0.016129
5686	13298	360.00	1	1	2	180.000000	1.0	0.010417	0.500000
5687	14569	227.39	1	1	5	18.949167	1.0	0.012658	0.083333
5688	83704	17.90	1	1	1	2.557143	1.0	0.071429	0.142857
5689	83705	3.35	1	1	1	1.675000	1.0	0.500000	0.500000
5690	83706	6637.59	1	1	23	10.452898	1.0	0.000572	0.001575
5691	83707	7689.23	0	1	22	10.518782	1.0	0.000497	0.001368
5692	83708	3217.20	0	1	20	54.528814	1.0	0.001529	0.016949
5693	83709	5664.89	0	1	16	25.985734	1.0	0.001366	0.004587
5694	12713	848.55	0	1	9	22.330263	1.0	0.001969	0.026316

Overview

Variables

Interactions

Correlations

Spearman's ρ

Pearson's r

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows